Modeling, Testing and Calibration of Ductile Fracture › icl › Research › Research Overview ›...
Transcript of Modeling, Testing and Calibration of Ductile Fracture › icl › Research › Research Overview ›...
8/7/2014 1 1Industrial Fracture Consortium 1/23
Modeling, Testing and Calibration of Ductile Fracture
1
8/7/2014 2 2Industrial Fracture Consortium 2/23
Lab facility
Custom-made biaxial testing machine MTS universal testing machine SHPB systems in France
INSTRON 9250HV
Three-point bending of a hat assembly
Tension−compression test
HydraulicVertical: 50 kNHorizontal: 25 kN
Electro-mechanical200 kN, 10kN
Max. vel: 20m/s
INSTRON 5944
2 kN, 100 NVic 2D and Vic 3D software, two digital cameras, high speed cameras,Abaqus, LS-DYNA, Hypermesh, workstations
8/7/2014 3 3Industrial Fracture Consortium 3/23
Plasticity
8/7/2014 4 4Industrial Fracture Consortium 4/23
Conventional metal plasticity
* Yield surface
- Von Mises yield criterion:
* Flow rule
- Associated flow rule:
(Plastic potential=yield function)
* Hardening law
- Swift law:- Voce law:- Extrapolation up to a large strain- Isotropic hardening
3( , ) ' : ' ( ) 0
2p pf k σ σ σ
0( ) ( )n
p pk A
p p
fd d
ε
σ
0( ) (1 exp( ))p pk k Q
0.0 0.2 0.4 0.6 0.8 1.00
400
800
1200
1600
Tru
e s
tress [
MP
a]
Equivalent plastic strain
Swift law
Voce law
Saturation type
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Von Mises yield criterion
k
k
8/7/2014 5 5Industrial Fracture Consortium 5/23
* Different anisotropy between yield stress and Lankford ratio (r-value),
Anisotropy and non-associated flow rule*
*Mohr et al. “Evaluation of associated and non-associated quadratic plasticity models for advanced high strength steel sheets under multi-axial loading, International Journal ofPlasticity, Vol. 26, pp. 939-956, 2010.
( , ) ( ) 0p pf k σ Pσ σ
( ) p
gg d d
σ Gσ σ ε
σ
Non-associated flow rule
( , ) ( ) 0p pf k σ Pσ σ
p p
fd d
ε
σ
Associated flow rule
w
t
dr
d
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Yield locus
Plastic potential
k
k
pdε
0
90
45
8/7/2014 6 6Industrial Fracture Consortium 6/23
Validation of non-associated flow rule
* Validation with DP590 and TRIP780
DP 590
TRIP 780
0
90
45
8/7/2014 7 7Industrial Fracture Consortium 7/23
Hardening curve after necking
* Fracture occurs after a significant amount of necking- Need for the stress−strain curve after necking- Non-uniform deformation in the gauge section after necking
→ hard to obtain hardening curve after necking experimentally
* ‘Inverse method’ using finite element simulation- Use of so-called ‘Notch tension test’ with R20 mm- Adjustment to the stress−strain curve in the post necking area until force
−displacement curve from simulation agrees well with the one from theexperiment
- It is unavoidable to repeat simulation
* Why ‘Notch tension test’?- Its geometry always generates necking exactly in the middle of specimen
because of the minimum gauge width there- Robustness and repeatability of tests
RW
8/7/2014 8 8Industrial Fracture Consortium 8/23
Procedure for inverse method
0.00 0.02 0.04 0.06 0.08 0.100
200
400
600
800
1000
1200
Tru
e s
tress [
MP
a]
Equivalent plastic strain
Experimental data
Swift law
Voce law
0( ) ( )n
Swift p pk A
0( ) (1 exp( ))Voce p pk k Q
A 1501
ԑ0 0.0002
n 0.123
k0 715
Q 400
β 37.9
1/8model
Displacement measuredwith DIC
0.0 0.2 0.4 0.6 0.8 1.00
400
800
1200
1600
Tru
e s
tress [
MP
a]
Equivalent plastic strain
Experimental data
Swift law
Voce law
Mixed Swift-Voce law
( ) ( ) (1 ) ( )p Swift p Voce pk k k
Mixed Swift−Voce law
: weighting factor
0.0 0.5 1.0 1.5 2.00
10
20
30
40
Fo
rce
[k
N]
Displacement [mm]
Experimental data
Swift law
Voce law
Mixed Swift-Voce law
Post necking region
Before necking
8/7/2014 9 9Industrial Fracture Consortium 9/23
Strain rate dependency*
*Roth and Mohr, “Effect of strain rate on ductile fracture initiation in advanced high strength steel sheets: Experiments and modeling”, International Journal of Plasticity, Vol. 56, pp. 19-44, 2014
0
0
0
[ , , ] [ ] [ ] [ ]
( ) ( ) (1 ) ( )
1 for
[ ]1 ln for
1 for T < T
[ ]1
p p p p T
p Swift p Voce p
p
p p
p
r
T r
m r
k T k k k T
k k k
kC
k T T T
T T
for T T T
m
r m
* Rate dependent hardening model
2
3
[ ] ( : Taylor-Quinney coefficient)
0 for
(3 2 )[ ] for
1
kp p k
p
p it
p it a p it
p it p a
a it
dT w dC
w
for a it
Input bar
Pusher
Stirrup
Specimen
Output bar 1
Output bar 2
Base plate
7,8,9: guide blocks
Experimental setup
Dependency of weighting factor on strain rate
8/7/2014 10 10Industrial Fracture Consortium 10/23
Plasticity model for reverse loading (MYU)
* Plasticity model for reverse loading (by Stephane Marcadet)
- Compression followed by tension or tension followed by compression- New behaviors should be incorporated into plasticity model
• Bauschinger effect
• Work hardening stagnation
• Permanent softening
- Kinematic hardening is used instead of isotropic hardening- Four parameters- Calibration of the model based on uniaxial tension followed by compression- Effect of four parameters
[ , , , ]
Bauschinger transition Stress level at stagnation Duration of stagnation Slope at post stagnation
8/7/2014 11 11Industrial Fracture Consortium 11/23
Novel experiment technique for plasticity
8/7/2014 12 12Industrial Fracture Consortium 12/23
Fracture model
8/7/2014 13 13Industrial Fracture Consortium 13/23
1 2 3
1 2 3 1 2 3
2 2 2
1 2 3 2
1
3
, , Load vector in Cartesian coord.
' , , Hydrostatic pressure vector
' , , , ,
2' 2
3
27det[ ]1cos
3 2
Carte
m m m
m m m
Mises
ij
Mises
OP
OO
O P s s s
O P s s s J
s
sian coord. Cylindrical coord. (Haigh-Westergaard coord.)
2cot , ( :Stress triaxiality)
3
61 , ( : Normalized Lode angle, 0 60 )
( , ) : Representing specific loading path
mp
<Principal stress space>
<Deviatoric 𝜋-plane>
Loading path parameter
* Formulation of stress triaxiality 𝜂 and Lode angle 𝜃
8/7/2014 14 14Industrial Fracture Consortium 14/23
History of fracture models at ICL
(1)Bao and Wierzbicki, “On fracture locus in the equivalent strain and stress triaxiality space”, International Journal of Mechanical Sciences, Vol. 46, pp. 81-98, 2004.(2)Bai and Wierzbicki, “Application of extended Mohr−Coulomb criterion to ductile fracture”, International Journal of Fracture, Vol. 161, pp. 1-20, 2010.(3)Mohr and Marcadet, “Hosford−Coulomb model for predicting the onset of ductile fracture at low stress triaxialities”, submitted for the publication.(4)Roth and Mohr, “Effect of strain rate on ductile fracture initiation in advanced high strength steel sheets: Experiments and modeling”, International Journal of Plasticity, Vol. 56, pp. 19-44, 2014.
Three-branch fracture model(1) Modified Mohr−Coulomb model (2010)(2) 3 3
2
1
2
11
3ˆ 1 sec 1
62 3
1 1cos sin
3 6 3 6
f
p
n
Ac c
c
cc
Extended Mohr−Coulomb model (2014)(3), (4)
11
1 2 2 3 3 1
1
1 3
0 0
0 0
0
1( , ) (1 ) (
2
2
for
1 ln for
a a af anp
n
p
p
p
b c f f f f f f
c f f
b
bb
0 ( , )
fp p
f
p
dD
8/7/2014 15 15Industrial Fracture Consortium 15/23
Calibration of fracture model
* Fracture tests5 types of tests characterizing a different combination of 𝜃 and 𝜂- NTR 20: notch tension with R20- NTR 6: notch tension with R6- CHD4: central hole with D4- Butterfly: tension & shear (plane strain tension & pure shear)- Punch: biaxial tension
NTR 20 NTR 6 CHD4
ButterflyPunch
8/7/2014 16 16Industrial Fracture Consortium 16/23
Identification of loading path
Experiment FE analysis Comparison
Displacement measuredusing DIC(VIC2D)
Two red points are symmetric
1/8 modelC3D8R
Extract loading path
Fracture initiation point
Optimization of fracture parameters
8/7/2014 17 17Industrial Fracture Consortium 17/23
Extreme bending of riser with fracture
Shear dominant fracture